Problem: The sum of two numbers is $43$, and their difference is $7$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 43}$ ${x-y = 7}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 50 $ $ x = \dfrac{50}{2} $ ${x = 25}$ Now that you know ${x = 25}$ , plug it back into $ {x+y = 43}$ to find $y$ ${(25)}{ + y = 43}$ ${y = 18}$ You can also plug ${x = 25}$ into $ {x-y = 7}$ and get the same answer for $y$ ${(25)}{ - y = 7}$ ${y = 18}$ Therefore, the larger number is $25$, and the smaller number is $18$.